In search for the social hysteresis -- the symmetrical threshold model with independence on Watts-Strogatz graphs.

We study the symmetrical threshold model with noise, interpreted as independence from the social point of view, within pair approximation as well as Monte Carlo simulations on Watts-Strogatz graphs. We show that the hysteresis increases with the average degree of a network k and rewriting parameter beta. On the other, hand the dependence between the width of the hysteresis and the threshold r, needed for the social influence, is non-monotonic, having an optimal value r in (0.65,0.85) for k observed in the real social networks. The value of the threshold r, for which the maximum hysteresis is observed, overlaps pretty well the size of the majority used for the descriptive norms in order to manipulate people within social experiments. We put results obtained within this paper in a broader picture and discuss them in the context of two other models of binary opinions, namely the majority-vote and the q-voter model.